Trigonometric store



oom m ow QOQ m 0% mok mow {k wi M INVENTOR. HE/PBER r N. FUL DNER l7TTORNEYS H. M. FULDNER TRIGONOME'IRIC STORE Filed Aug. 30. 1960 5 O .N mO\\ U\ O u o k WN 0? April 6, 1965 United States Patent 3,177,423TRHGQNOMETREC STGRE Herbert M. Fuldner, Fort Thomas, Ky, assignor to TheCincinnati Milling Machine Company, Cincinnati, (Phio, a corporation ofOhio Filed Aug. 30, 1960, Ser. No. 52,992 6 Claims. (Cl. 323-435) Thisinvention relates to a converter for transforming digital informationinto analog voltages which are representative of the desired positionsto be assumed by the numerical controlled element of a machine tool.More particularly, the invention relates to a circuit for convertingdigital information into angular data corresponding to the rotation of ashaft, the converted data being in the form of quadrature voltages whichare proportional to the sine and cosine of the angle of rotation.

It is known to provide trigonometric stores of the type which convertdigital input information into angular data such as sine and cosinevoltages and thereafter to apply these voltages to the quadraturewindings of a resolver which serves as the error detecting device of aservo system. One such device is shown and described in the US. Patentto Tripp, No. 2,849,668, granted August 26, 1958, for Automatic MachineControl. The purpose of the present invention is to simplify the priorart apparatus by reducing the size and number of transformers andswitches required thereby reducing the cost and complexity of thesystem. A further purpose of the present invention is to combine asystem of 36 segments or bites with a system of 18 bites so as to obtainin one system the advantages of the two individual systems. This isaccomplihsed by providing a sine-cosine transformer with five 18 taps oneither side of a center tap. The output of the transformer is obtainedby a tap switch which advanoes in 36 steps. Each 18 segment of the 36step is then individually interpolated into five equal parts to obtainthe 3.6 increments. These increments are in turn divided into ten equalparts to obtain the .36 increments.

Accordingly, it is an object of the present invention to provide animproved type of trigonometric store which is simpler and less costly toconstruct than former devices of this character.

Another object of the invention is to provide a trigonometric storehaving a tapped sine-cosine transformer of relatively few turnswhile'providing a high degree of accuracy in the synthesis of the sineand cosine voltages.

Another object of the invention is to provide a trigonometric storewhich utilizes split linear interpolation for the subdivision of theangles represented by the sine and cosine Voltages derived from t aps ona sine-cosine transformen Another object of the invention is to proivdea digitalto-angular data converter which has all the advantages of asystem employing 36 segments while affording the accuracy of a systememploying 18 segments.

With these and other objects in view which will become apparent from thefollowing description, the invention includes certain novel features ofconstruction and combination of parts, the essential elements of whichare set forth in the appended claims, and a preferred form or embodimentof which will hereinafter be described with reference to the drawingswhich accompany and form a part of this specification.

In the drawings:

FIG. 1 is a diagram of the trigonometric store as incorporated in aservo system.

FIG. 2 is a diagram of the switching circuit used to I change'theconnections from one pair of switch banks to another.

EJ711423 Federated Apr. 6, 1965 In the-circuit shown in the accompanyingdrawings, an AC. reference voltage is applied to terminals 10 and 11which are connected by conductors to the end terminals 12 and 13 of atapped autotransformer 14. Since, in the present apparatus, theautotransformer is required to serve as a low-impedance, precisionvoltage divider, it is preferably a toroidal type transformer designedfor minimum flux leakage between turns. As shown, the transformer iswound on an annular core 15 and is provided with a grounded center tapand eight intermediate taps 17, which are appropriately spaced toprovide voltages which are proportional to the sine and cosine of 0, 18,36, 54, 72, and 90 on either side of the center tap, the sine of 0 beingequal to the cosine of 90, the sine of 18 being equal to the cosine of72, the sine of 36 being equal to thecosine of 54, etc.

In designing the transformer 14 it was found that in order to providevoltages which were accurate to within one part in 100,000 of the sineand cosine voltages required, a transformer of approximately 100,000turns would be required. Since such a transformer would be not only verycostly but also of very high impedance due to the amount of wirerequired, it was necessary to devise some other means for obtaining thedesired degree of accuracy. In the present instance this has beenaccomplished by the use of a second toroidal transformer 20 having anannular core 21 on which is wound a primary winding 22 and eightsecondary windings 23. The secondary windings are inserted in the leadsfrom the taps 17 and thereby act to insert correcting voltages whicheither add to or subtract from the voltages provided by the taps. Tomaintain the proper phase relation between the injected voltages and thevoltages from the taps, and also to maintain the proper amount ofvoltage injection regardless of variations in the supply voltage, theprimary winding 22 is excited from a winding 24 wound on the core 15 ofthe autotransformer.

In the present embodiment of the invention, the transformer 14 isprovided with 252 turns, i.e., 126 turns on either side of the centertap 100, and the taps for sine 18, 36, 54 and 72 are tapped at 39, 74,102 and turns respectively, on either side of the center tap. Theprimary winding of transformer 20 is provided with 48 turns and thesecondary windings connected to terminals E, D, C, B have 3, +3, -3 and-8 turns, respectively, as do also the secondary windings connected toterminals G, H, I, and K, respectively. The signs as used above indicatethat the secondary windings are poled to subtract their voltages fromthose provided by the transformer taps, while the sign indicates thatthis winding'is poled to add its voltage to that provided by the tap.The winding 24 which excites the primary winding of transformer 20 iscomprised of a single turn wound on the core 15. It will be appreciatedthat multiples of the given numbers of turns will provide the samevoltages at the terminals AL but with a higher impedance.

Accordingly, when the terminals 10 and 11 are energized from a source ofreference voltage, terminals 25, marked A-L will be supplied withvoltages which are proportional to the plus and minus values of the sineand cosine of 0, 18, 36, 54 72 and 90.

Assuming that the feedback unit connected to the machine tool elementwhich, in the present instance, is assumed to be a slide, is one whichis subject to angular displacement such as, for example, a resolver, andthat .1 inch movement of the slide produces one revolution or 360rotation of the feedback unit, then each 36 of displacement of the unitwill equal .01 inch movement of the slide. Thus, 36 divisions of thetransformer 14, such as between terminals F and D, D and B, etc. Willrepresent .01 inch of slide movement. Since, in the present ap enemas 1In other words, the voltage between taps on the winding 29 is ten timesas great as the voltage between taps on the winding 30. This is for thepurpose of enabling the voltage between adjacent terminals A, B, C, D,etc. to be dividedinto five equal parts by winding 29 with each. ofthese divisions then being further resolved into ten equal parts by thewinding 30. The means for connecting the taps in the proper order toprovide the desired resolution of voltages comprises three multi-bankswitches 138, 258 and 3S8. These may be manually settable selectorswitches or, alternatively they may take the form of step ping switchescontrolled from a punched tape and tape reader in a well-known manner.

As above noted, the switches are provided with multiple banks ofcontacts which are designated by letter suffixes such as C, B, E, etc.As herein illustrated, the switch bank llSS-C has ten contacts numbered9, inclusive, which contacts are connected to the terminals in the orderindicated by the letter designations beside the contacts, namely, F, D,B, B, D, F, H, K, K, H. It will be noted that these are alternateterminals. in other'words, the wiper of bank lSS-C advances in 36 bites.

Bank D of switch 158 has its ten contacts 0-9 connect ed to theterminals 25 as indicated by the letter designation beside the contacts,namely, E, C, A, C, E,G, J, L, J, and G. These too it will be noted arealternate terminals on the transformer. However these terminals liebetween the terminals to which the contacts of bank 1SS-C are connected,i.e., the order of connection has been advanced 18. terminals'D, B, B,D, F, H, K, K, H and B. These are the same terminals to which thecontacts of banks lSS-C are connected but the order of connection hasbeen advanced 36. Hence, when the wipers of switch 183 are on 0, a wired2 connected to the wiper or" bank C will be Bank E of switch 188 hasten contacts connected to per end of winding 29 and a voltageproportional to the sine of 36 will be supplied to the lower end of thewinding. The voltage impressed across the winding 29 represents,therefore, the angular span from 18 to 36 in terms of the sine function,and thisspan is divided into five equal parts by the taps 74-73representing the digits .005 to .009. Each of these divisions is in turndivisable into ten equal parts by the taps on winding 30.

When the thousandths digit changes from 9 to 0, relay 20R is againdeenergized and wires 92 and 94 are again connected to wires 74 and '70,thereby again connecting the first 18 segment of the 36 bite to thewinding 29. It will now be seen that each step of switch KSSVCQIIE-sponds to a 36 bite and that each bite is divided into two 18 segments.

The approximate value of the cosine of 195.12" is derived in a similarfashion from the sine-cosine voltages 7 provided at the terminals A-L.For this purpose there is connected to ground, a wire 9 connected to thewiper of bank D will be supplied with a potential proportional to thesine of 18 and a wire 95 connected to the wiper of bank B will besupplied with a potential proportional to the sine of 36. The wires 92',9 2- and 95 are connected to a pair of wires '74 and 79 through thecontacts of a I switching relay ZCR. When the relay is deenergized, thewires 92 and 94 are connected to the wires '74 and '79, respectively,which, in turn, are connected to the terminals of the winding 29 ontransformer-2h. Hence, a volt age proportional to the value of sine 18is impressed across the winding 2?.

The taps of winding 29 are connected by wires 74 -725 to the contacts0-9' of a switch bank LESS-D. As indicated on the drawing, wire 74 isconnected to the contacts 0 and 5, wire '75 is connected to contacts 1and 6, etc. '1 .e taps of winding 30 are connected to the contacts 0-9of a switch bank dSS-C, and a wire 91 connects the wiper of this bankwith the wiper of bank ZSS-D. An output con ductor $1 is connected tothe end of winding 3d which is connected to the 0 contacts of switchbank SSS-C and provides anoutput voltage which, referenced to ground,

is approximately proportional to the sine of the angle corresponding tothe decimal amount setup on the switches 188, 253 and 38S. When theseswitches are set to the positions indicated in the drawings, i.e., .0542inch, the

corresponding angle is 195.12. Whenthe thousandths digit'changes from 4to 5, relay ZCR is energized through bank C of switch 285 (FIG. 2thereby connecting wire 94 to wire 74 andwire 95 to wire 79; Hence, avoltage 2 proportional to the sine of 18 will be supplied to the-upprovided a second toroidal transformer 33 which may be identical to thetrmsforrner 28 and, like this transformer, has a pair of linearly tappedwindings Maud 35 wound on an annular core .36. The winding 34 is dividedinto five sections of twenty turns each and the winding '35 is dividedinto ten sections of two turns each so that the voltage between taps onwinding Ed is ten times as great i as the, voltage between taps onwinding 35.

The data input meansfor the cosine system includes additional banks ofcontacts on the switches 13S, 23S and 388. For example, banks F, G, andH of switch 183 are connected to terminals A-L according to the samescheme as used for the sine functions but displaced to provide voltageswhich are proportional to the cosine of the angle. When relay ZCR isdeenergized, wires 1% and 104 are connected to wires )6 and 1.02, which,in turn, are connected to the upper and lower ends of the winding 34.Hence, a voltage proportional to the cosine value of the first 18segment of a 36 bite wiil be impressed across the winding 34. The fivetaps of this winding are connected by wires 96-101 to the contacts 09'ofa switch bank ZSS- E, wire 96 being connected to contacts 0 and 5. wire97 being connected to contacts 1 and 6, etc. The taps of winding 35 areconnected to the contacts 09 of a switch bank ESS-D and a wire 116connects the wiper of this bank with the wiper of bank ZSS-E. An outputconductor 1536 is connected to the 0 end of winding 35 and true sine andcosine values of the 3.6 and 36 angular 7 increments which correspond tothe .001 inch and .0001 inch movements of the slide. It has beendiscovered, however, that the ratio of the sine and cosine values, i.ethe tangent function of the angle, is remarkably accurate in spite ofthis approximation. This resultsfromthe fact that when the sine andcosine values thus produced are supplied to the quadrature windings of asine-cosine type of feedback unit, such as a resolver, it is the ratioof the sine and cosine values which determines the position taken up bythe device." Hence, it is responsive to the tangent of the angle andbyuse of the transformers 1d and 2b, as described, which produce verynearly true values of the sine and cosine functions at 18 intervals, itis possible with the present system to obtain values of thetangentfunction which are accurate to within two minutes of angle. Since twominutes is equal to approximately .00001inch of slide movement, thetrigonometric store herein described is well within the limits ofaccuracy needed; for controlling slide movement to the nearest,0001inch. A seven-fold increase in accuracy is obtainable by the use of18 increments in place of 36 increments. In

other words,;had a 36 bite system per se been used Vin place of thecombined 18 and 36 system disclosed herein, the values of the tangentfunction would have been accurate only to within 14 minutes or .00007inch of slide movement. Since it is desirable in the present controlsystem to maintain an accuracy of .0001 inch of slide movement, thefactor of safety using a straight 36 system would be undesirably small.

As shown in FIG. 1, the sine and cosine voltages are applied to theguadrature windings 70, 71 of a resolver 72 which is also provided witha rotor winding 73. The two leads 84 and 85 from this winding areconnected to a pair of input terminals on a servo-amplifier 86. Theoutput of the servoamplifier is connected by leads 87 and 88 to thecontrol winding 89 of a two-phase electric servomotor 90. This motoralso is provided with a reference voltage winding 91 and runs in onedirection or the other depending on the phase of the voltage supplied tothe winding 89 in a well-known manner. The armature of the motor isdrivingly connected, as indicated by the dashed line 107, to the slide93 which is to be positioned in accordance with the input data suppliedto the trigonometric store. The rotor of the resolver is also arrangedto be driven by the slide through an angle of 36 for each .01 inchmovement of the slide as is indicated by the dashed line 108.

When the rotor of the resolver is turned by the motor to a position inwhich the voltage across the leads 84 and 85 is reduced to zero, thenthe output of the servoamplifier will also be reduced to zero, and theservomotor will be deenergized. This will stop the slide 93 in theposition required by the input data.

While the present system has been shown applied to a single informationchannel only, namely the fine channel of a control system, it will beappreciated that the principles of the invention may be applied withequal advantage to the other information channels of the control system,for example, to the coarse and medium channels, in accordance with theknown practices of the prior art.

Having thus described the invention in connection with one possible formor embodiment thereof and having used, therefore, certain specific termsand language herein, it is to be understood that the present disclosureis illustrative rather than restrictive and that changes andmodifications may be resorted to without departing from the spirit ofthe invention as defined by the claims which follow.

What is claimed is:

1. A trigonometric store for a positioning system comprising a functiongenerating transformer including a plurality of voltage taps selected toprovide a series of voltages proportional to the values of the sine andcosine of angles spaced at 18 intervals, an interpolating transformerhaving two linearly tapped windings each capable of dividing a voltageimpressed thereacross into equal voltage increments, one of saidwindings having ten times as many turns between taps as the otherwinding, switch means for connecting a selected pair of adjacent taps onsaid function generating transformeracross said one winding, andadditional switch means for connecting a selected tap on said onewinding with a selected tap on said other winding to thereby cause avoltage to be impressed on one end of said other winding which isapproximately proportional to the value of the sine or cosine of theangle represented by the setting of said switch means.

2. A trigonometric store comprising a function generating transformerhaving a plurality of voltage taps selected to provide a series ofvoltages approximately proportional to the value of the sine and cosineof a plurality of equally spaced angles, an injection transformer havinga single primary winding and a plurality of secondary windings eachhaving one end connected to a tap on said function generatingtransformer, a winding on said function generating transformer forenergizing said primary winding, an interpolating transformer having alinearly tapped winding for dividing a voltage impressed thereacrossinto equal voltage increments, switch means for connecting the otherends of a selected pair of adjacent secondary windings across saidlinearly tapped winding, and additional switch means for selecting avoltage from any one of the taps of said linearly tapped winding tothereby provide a voltage which is approximately proportional to thevalue of the sine or cosine of the angle represented by the setting ofsaid switch means.

3. A trigonometric store comprising an autotransformer of two hundredfifty-two turns with a center tap and first, second, third, and fourthtaps at 39, 74, 102 and 120 turns on either side of the center tap, aninjection transformer having a primary winding of forty-eight turns andfirst, second, and third and fourth secondary windings each having oneend connected to a corresponding tap on said autotransformer and having-3, +3, -3 and -8 turns respectively, and a winding of one turn, or amultiple thereof, on said autotransformer connected to said primaryWinding for energizing the same.

4. The trigonometric store of claim 3 including an interpolatingtransformer having a linearly tapped winding for dividing a voltageimpressed thereacross into equal voltage increments, switch means forconnecting the other ends of a selected pair of adjacent secondarywindings across said linearly tapped winding, and additional switchmeans for selecting a voltage from anyone of the taps of said linearlytapped winding to thereby provide a voltage which is approximatelyproportional to the value of the sine or cosine of the angle representedby the setting of said switch means.

5. A trigonometric store comprising a function generating transformerhaving a plurality of voltage taps selected to provide -a series ofvoltages proportional to the values of the sine and cosine of anglesspaced at 18 intervals from 0 to and from 0 to 90, an interpolatingtransformer having a linearly tapped winding capable of dividing avoltage impressed thereacross into equal voltage increments, switchmeans for selectively connecting either of two pairs of three adjacenttaps on said function generating transformer across said linearly tappedwinding, additional switch means cooperating with the taps on saidlinearly tapped winding, and means controlled by said additional switchmeans for causing said first mentioned switch means to disconnect one ofsaid pairs of taps from across said linearly tapped winding and toconnect the other of said pairs of taps thereacross.

6. The trigonometric store of claim 5 wherein said first mentionedswitch means includes a switch having at least three banks of contactswith successive contacts on each of the three banks connected toalternate taps on said function generating transformer and with thecorresponding contacts of each bank connected to taps spaced 18 apart.

References Cited by the Examiner UNITED STATES PATENTS 1,667,752 5/28Thomas 323-43.5 2,200,979 5/40 Blume 323-435 2,201,642 5/40 Bauer323-435 2,849,668 8/58 Tripp 323-435 3,042,307 7/62 Booth et a1. 235-197X LLOYD MCCOLLUM, Primary Examiner. ORIS L. RADER, Examiner.

1. A TRIGONOMETRIC STORE FOR A POSITIONING SYSTEM COMPRISING A FUNCTIONGENERATING TRANSFORMER INCLUDING A PLURALITY OF VOLTAGE TAPS SELECTED TOPROVIDE A SERIES OF VOLTAGES PROPORTIONAL TO THE VALUES OF THE SINE ANDCOSINE OF ANGLES SPACED AT 18* INTERVALS, AN INTERPOLATING TRANSFORMERHAVING TWO LINEARLY TAPPED WINDINGS EACH CAPABLE OF DIVIDING A VOLTAGEIMPRESSED THEREACROSS INTO EQUAL VOLTAGE IMCREMENTS, ONE OF SAIDWINDINGS HAVING TEN TIMES AS MANY TURNS BETWEEN TAPS AS THE OTHERWINDING, SWITCH MEANS FOR CONNECTING A SELECTED PAIR OF ADJACENT TAPS ONSAID FUNCTION GENERATING TRANSFORMER ACROSS SAID ONE WINDING, ANDADDITIONAL SWITCH MEANS FOR CONNECTING A SELECTED TAP ON SAID ONEWINDING WITH A SELECTED TAP ON SAID OTHER WINDING TO THEREBY CAUSE AVOLTAGE TO BE IMPRESSED ON ONE END OF SAID OTHER WINDING WHICH ISAPPROXIMATELY PROPORTIONAL TO THE VALUE OF THE SINE OR COSINE OF THEANGLE REPRESENTED BY THE SETTING OF SAID SWITCH MEANS.